Algebraic Geometry Sundance 1986: Proceedings of a by Audun Holme, Robert Speiser

By Audun Holme, Robert Speiser

This quantity offers chosen papers as a result of the assembly at Sundance on enumerative algebraic geometry. The papers are unique study articles and focus on the underlying geometry of the subject.

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Additional info for Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986

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Contains exactly hO~oc~5-r) ÷ r - I (resp. hO~o C' ÷ r - I ) independant quadrics. iii) The homogeneous ideal of C is generated by quadrics iff the multiplication maps H0wc~5-r) ® HOOc~k) -~ H0coC~5-r*k) (resp. H0~C ' @ HOOc~k) -* H0~c~k) ) are surjective for all k>O. 7: If C is a reduced and irreducible locally Gorenstein curve of arithmetic genus >0, and L is a line bundle generated by its global sections with hO(L)_~5, then the module ~HO(y_ -" L n) is generated, over the ring ~H OLn bV elements of degree i O.

3) above A, B and C are themselves rational 28 linear c o m b i n a t i o n s of CU, TN, TR and the b o u n d a r y c o m p o n e n t s this is e q u i v a l e n t to &0 and Ai, J, Conjecture'. The Picard group of the v ~ r i e t y V of nodal q u r v e s is torsion. The purpose of t h e present p a p e r Is twofold, First, in t h e following sectlon, we will p r o v e t h a t w i t h the exception of the cases g = 0 or ! and 8 = 0 , 1 or 2, the divisor classes A, B, C a n d A a r e indeed independent.

4) a n d t h e p a p e r of Eisenbud a n d Harris [1987]. I: Let_C ¢ pr be a curve. If C is s c h e m e theoretically cut out by hv1oersurfaces of deeree e, and if C is contained in s o m e two-dimensional rational normal scroll in pr, then the homogeneous ideal of C is generated by forms of degree ~_ e. R e m a r k : We allow t h e possibility t h a t t h e scroll m a y be singular, a n d r e q u i r e of C only t h a t it be a p u r e l y 1-dimensional s u b s c h e m e . i m a y be applied in several situations.

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